This is the tool you need to draw a vacuum on the system and then let it suck the coolant in.
This tool will not work as you do not have the space to insert it in the radiator cap opening.
I use the Mityvac MV4535 Cooling System AirEvac Kit that I had to modify the rubber cone fitting by using a 90 degree 1/4 inch pipe thread elbow to which I epoxied the chrome fitting to and the other end I use a 1/4 inch pipe thread to barbed fitting. This provides the proper clearance to do the job. I used it on my K1600GT this spring to do the 18,000 miles maintenance and also lend it to my friend to do his K1600GTL.
A not of caution when doing the maintenance, you have to remove the plastic pipe on top of the valve cover. Do not follow the service manual instruction for this as you will break that pipe and it will cost you ~$100 for a replacement. The safe alternative is to use a thin bit holder ratchet with the proper bit (You will need to cut about 3/16 inch from the torx bit hex end to get the proper clearance) and remove the screw securing the 3 aluminium covers that the pipe connects to.
Since your radiator is removed, get it to a radiator shop and ask them to clean the outside of the core by soaking it, this will get your running temp back to normal.
For the replacement Anti-freeze, go to your local BMW Car dealer and buy a gallon of the anti-freeze (Paid $23.00CDN for 3.8Litres at my local dealer) (it's the same as they use in the motorcycle), Also buy 1 gallon of Distilled or De-Ionized Water to mix with the Anti-freeze in a 50/50 mix. Find a clean container that holds 1 gallon and mix the Anti-freeze and Water before use.
For the spark plugs, here is a ling to order them for $12.06 each; https://www.ngk.com/product.aspx?zpid=46681
You will have to plan about 6 hours to do the 18,000 mile maintenance (Engine Oil and filter change, Final Drive oil Change, valve clearance check and spark plug replacement